The visitors were camped in their opponents' half for long periods but were frustrated by a combination of their own lack of a cutting edge and Swansea's diligent defending, before Dele Alli eventually broke through to convert Christian Eriksen's cross after 88 minutes.

Son Heung-min fired Tottenham ahead in added time, and then Eriksen completed the remarkable comeback with a curling effort.

While second-placed Spurs continue to breathe down the necks of leaders Chelsea, a third defeat in four games sees Swansea drop into the relegation zone.

Tottenham leave it late

Christian Eriksen has been directly involved in 10 goals in his seven Premier League games against Swansea (6 goals, 4 assists)

Having cut Chelsea's lead at the top of the table to seven points with Saturday's win at Burnley, Spurs were aiming to further reduce that deficit with a fifth successive Premier League victory.

Yet for all that Mauricio Pochettino's side had impressed this season, that triumph at Turf Moor was only their fifth away league win - and their vulnerability on the road was evident at the Liberty Stadium.

Although they enjoyed near total control of possession and territory during a one-sided first half, Tottenham fell behind after Swansea's first attack of the game.

Jordan Ayew muscled his way into the visitors' penalty area and pulled the ball back to Routledge, one of four former Spurs in the hosts' line-up, and the winger squeezed his finish past ex-Swans keeper Michel Vorm.

Tottenham had 73% of possession at the Liberty Stadium, much of which they held inside the Swansea half as their heatmap (right) shows

Tottenham continued to boss proceedings but lacked a cutting edge in attacking positions, missing injured top scorer Harry Kane and frustrated by their dogged opponents.

But as they had demonstrated in their previous seven games without Kane - four wins and three draws - Spurs can cope in the striker's absence.

They left it late, with Alli tapping into an empty net from Eriksen's wicked low cross, before Son finished from close range to send the visiting Spurs fans into raptures.

Eriksen then added a third in added time to complete a stunning fightback and leave their opponents crestfallen.

Swansea's worries deepen

Hull's win over Middlesbrough sends Swansea back into the bottom three

A return of just one point from their previous three games had seen Swansea sink deeper into relegation trouble, one point and one place above the bottom three.

Head coach Paul Clement spoke of a nervousness inside the Liberty Stadium during Sunday's goalless draw with Middlesbrough, though any creeping sense of anxiety for the home fans was eased with Routledge's early goal.

They made their ground a cauldron of noise, roaring their approval with every tackle, block or pass from a Swansea player.

The hosts dared to attack on occasion, with Kyle Naughton close to becoming the second ex-Spurs player to score against his former employers as his deflected shot fizzed wide.

But it was Swansea's defensive effort which provided the foundation for their admirable display, and looked set to earn them a first league win over Spurs since 1982.

However, their resistance was eventually broken and, with relegation rivals Hull beating Middlesbrough, the Swans' descent back into the bottom three leaves their hopes of survival in doubt.

Man of the match - Dele Alli (Tottenham)

Despite their frustration at being held by Swansea, Spurs did not panic - and their calm was personified by Alli, who popped up in the perfect position to equalise.

Swansea have never beaten Spurs in the Premier League - the stats you need to know

Tottenham Hotspur (29) have won more points in 2017 than any other Premier League team (W9 D2 L1).

Spurs have won 17 points from losing positions in the Premier League this season; more than any other side in the competition.

In fact, under Mauricio Pochettino Tottenham have won 53 points from losing positions - 13 more than any other Premier League side in that time.

Swansea have never beaten Tottenham in 12 matches in the Premier League, drawing two and losing 10.

No Premier League team has scored more 90th minute winning goals this season than Tottenham (3 - level with Arsenal).

Dele Alli has been involved in 13 goals in 12 Premier League games for Tottenham in 2017 so far (9 goals, 4 assists).

Alli has yet to lose a Premier League game in which he has scored, winning 16 and drawing five. Christian Eriksen has been directly involved in 10 goals in his seven Premier League games against Swansea (6 goals, 4 assists).

Wayne Routledge made his 182nd Premier League appearance for Swansea City; more than any other player in the competition.

Routledge scored his first Premier League goal at the Liberty Stadium since Dec 2014, ending a run of 33 apps there without one.

'This season we are fighting again' - What they said

Media playback is not supported on this device

Clement reflects on 'heartbreaking' Swans defeat

Swansea manager Paul Clement: We are clearly very disappointed to get to 88 minutes leading 1-0 - we had a good chance at 1-0 as well.

"We continued to defend well and limit them. The fact we conceded on 88 and then couldn't even draw is heartbreaking.

"You still have to do all the things we had done. We were fatigued at the end but the lads gave everything and I am proud of them. We can't feel sorry for ourselves. We have two massive games now at West Ham and Watford."

Tottenham manager Mauricio Pochettino: "We started the game very well and created some chances in the first few minutes. In that moment I think we feel the game is going to be easy. The perception from the touchline was that the players started to play at a low tempo. When we concede the goal we realise we need to push and increase our level.

"How the goals arrived at the end was crazy but we pushed, we played better and we created chances to win. It is a good example of the team never giving up and trying to the end. Big credit to the players, they showed big character.

"The most important thing is the badge. When you play for Tottenham it is not about the names it is about the team and the spirit. You would like to have all your players available but this season we are showing we are a team."

What next?

Swansea face two big Premier League away games, at West Ham this Saturday, followed a week later by a trip to Watford.

Tottenham are at home against the Hornets this Saturday and then host Bournemouth on the 15th.